From repeated photoconductor testing: \(1\,\mathrm{kHz}\) and \(10\,\mathrm{kHz}\) were useful because they were measured consistently across devices. They are examples, not universal constants. The value comes from comparing the same lower and higher points under the same conditions.

A full noise spectrum contains far more information than two measurements. It can reveal the low-frequency rise, the flatter generation-recombination region, the GR rolloff, narrow interference peaks, and the eventual system or Johnson floor.

But repeated detector testing often produces noise values at the same small set of frequencies. A simple ratio can turn two routine measurements into a useful screening heuristic.

The ratio does not identify a microscopic mechanism. It answers a narrower question: is the lower-frequency noise elevated relative to a higher flat-band reference?

Two-frequency noise ratio
\[ r_{L/H}=\frac{e_n(f_L)}{e_n(f_H)} \]

Noise amplitude spectral density at the lower frequency divided by the higher reference.

What the number means

A ratio adds spectral shape to an absolute noise value

A noise value at \(f_H\) gives the detector's absolute noise level at that frequency. It does not show whether the spectrum remains flat as frequency decreases.

The ratio \(r_{L/H}\) adds that missing information:

\(r_{L/H}\approx 1\)

Noise is approximately flat between the selected frequencies.

\(r_{L/H}>1\)

The lower-frequency point is elevated; low-frequency excess noise may be entering the test band.

\(r_{L/H}<1\)

The higher-frequency point is elevated; check interference, resonance, or another readout feature.

Always report the ratio with an absolute noise value

The minimum useful comparison is the pair \(\{e_n(f_H),\,r_{L/H}\}\). A ratio near unity does not mean the detector is quiet; it only means the two selected points are similar.

There is no universal pass/fail value. The most useful reference is usually the distribution produced by comparable detectors measured with the same procedure.

Why two points help

Two detectors can look equal at one frequency and very different at another

Suppose two detectors have nearly the same noise at the higher reference frequency. A single-frequency comparison would treat them as similar. At the lower frequency, however, one detector may remain nearly flat while the other is noticeably elevated.

Linear two-frequency comparison of two detectors with similar high-frequency noise but different low-frequency noise
Illustrative two-point comparison. The NASD axis is linear and begins at zero. The horizontal spacing is schematic: only \(f_L\) and \(f_H\) are evaluated. Each endpoint is labeled with its measured noise density, and the connecting segments are guides to the eye.
Illustrative detector comparison
Detector \(e_n(f_L)\)\(\mathrm{nV}/\sqrt{\mathrm{Hz}}\) \(e_n(f_H)\)\(\mathrm{nV}/\sqrt{\mathrm{Hz}}\) \(r_{L/H}\) Immediate read
Detector A10.810.01.08Nearly flat
Detector B19.411.31.72Low-frequency rise

Worked calculation

Detector A\[ r_{L/H,A}=\frac{10.8}{10.0}=1.08 \]
Detector B\[ r_{L/H,B}=\frac{19.4}{11.3}=1.72 \]

The two detectors have similar noise at \(f_H\), but Detector B rises much more strongly toward \(f_L\). The ratio exposes that difference immediately.

The ratio is particularly useful across detector populations, where it can identify outliers that deserve a full frequency sweep.

Repeatability

A difference from unity must exceed measurement variation

Interpret \(r_{L/H}-1\) relative to repeated measurements. A small departure from unity is not physically meaningful when it is comparable to drift, temperature variation, bias instability, or the statistical spread of the noise estimate.

For screening work, report the mean ratio, the spread across repeats, and the number of measurements. Population limits should come from comparable detectors measured with the same procedure—not from a universal threshold.

Optional uncertainty propagation

If the two noise estimates are treated as independent, a first-order estimate is

\[ \left(\frac{\sigma_r}{r_{L/H}}\right)^2\approx \left(\frac{\sigma_L}{e_n(f_L)}\right)^2+ \left(\frac{\sigma_H}{e_n(f_H)}\right)^2. \]

Use the actual repeatability data when the two measurements share correlated drift or common calibration errors.

Frequency selection

The frequencies are chosen by function, not by convention

The method is general. Use a lower comparison frequency \(f_L\) and a higher reference frequency \(f_H\). Under a healthy baseline, both points should lie in the established flat GR measurement region. The heuristic becomes useful when excess low-frequency noise raises \(e_n(f_L)\) while \(e_n(f_H)\) remains a stable reference.

Higher reference: \(f_H\)

Choose a point in the established flat GR region, below detector or readout rolloff and away from isolated interference.

Lower comparison: \(f_L\)

Choose a lower point that is normally still in the flat region, but close enough to the low-frequency side to respond when the low-frequency crossover shifts upward.

In repeated photoconductor measurements, \(1\,\mathrm{kHz}\) and \(10\,\mathrm{kHz}\) are convenient examples. Their usefulness comes from repeatability and their location in the measurement band—not from any fundamental property of those exact values.

Important: the ratio does not require an exact \(1/f\) law. Two measured points are compared directly; no spectral exponent is assumed.

Connection to the spectrum

The ratio is related to the low-frequency crossover

Use \(f_{\times}\) for the crossover between a fitted low-frequency excess-noise trend and the flat GR reference level. For a noise amplitude spectral density fit, write the low-frequency branch as \(e_n(f)=A f^{-\beta}\), where \(A\) and \(\beta\) are obtained from the measured spectrum rather than assumed.

Synthetic logarithmic photodetector noise spectrum with a blue measured-like trace and magenta low-frequency and flat-GR fits intersecting at the crossover frequency
Synthetic illustrative spectrum. The magenta asymptotes are \(e_n(f)=A f^{-\beta}\) and \(e_n(f)=e_{n,\mathrm{GR}}\); their intersection defines \(f_{\times}\). The exponent is fitted from the data. The higher-frequency GR rolloff is outside the plotted range.

The two-frequency heuristic does not measure \(f_{\times}\). It flags when the crossover may have moved high enough to affect the lower comparison point:

  • If \(f_{\times}\ll f_L\), both selected points may remain in the flat region and \(r_{L/H}\approx 1\).
  • If \(f_{\times}\) approaches or exceeds \(f_L\), \(e_n(f_L)\) can rise while \(e_n(f_H)\) remains a useful reference, producing \(r_{L/H}>1\).
  • A full spectrum is still required to distinguish a broad low-frequency rise from narrowband interference or another frequency-dependent process.

This is why the ratio works as a screening quantity: it does not replace the spectrum; it identifies which devices deserve a full sweep.

HgCdTe application

Use the ratio as a population variable, not a universal MCT specification

Best use in HgCdTe photoconductors

Track \(r_{L/H}\) together with \(e_n(f_H)\) across passivation conditions, wafer position, device geometry, bias, temperature, and fabrication lot. A shift in the population distribution is more informative than an isolated value from one detector.

Published HgCdTe photoconductor measurements have shown that low-frequency noise can depend strongly on passivation and inferred surface-trap density. That supports using an elevated ratio as a screening flag, but it does not make the ratio a unique diagnosis of surface noise. [1]

Physical interpretation

What an elevated ratio may flag

An unusually large ratio within a comparable detector population can be consistent with several device or measurement problems:

Surface and fabrication

  • passivation changes;
  • surface or interface traps;
  • process damage or nonuniformity.

Device and operating point

  • contact-related fluctuations;
  • current crowding;
  • bias dependence or self-heating.

Measurement system

  • slow thermal drift;
  • bias-source contamination;
  • pickup or readout features.

The ratio is a flag, not a diagnosis. Bias sweeps, temperature dependence, full spectra, geometry comparisons, contact studies, and passivation experiments are what separate the possible causes.

Measurement validity

The ratio is only useful when both points belong to the detector

Keep the test chain quieter than the device.

Both values must be noise amplitude spectral densities normalized with the correct ENBW; raw RMS values are not directly comparable. Hold detector temperature, bias, resistance, optical condition, preamplifier gain, and averaging procedure constant. Battery-based bias, an appropriately matched low-noise preamplifier, short shielded wiring, disciplined grounding, and a Faraday cage help keep bench noise below the detector.

These controls do not define \(r_{L/H}\). They determine whether the ratio reflects detector behavior rather than the measurement system.

Reporting

A compact comparison record

A useful record contains the two measured noise densities, their ratio, and enough operating information to reproduce the comparison:

Noise data\(e_n(f_L)\), \(e_n(f_H)\), \(r_{L/H}\), repeatability, number of repeats
Operating pointtemperature, bias, resistance, optical condition
AcquisitionENBW, preamplifier, gain, averaging, filter settings

Always report the absolute reference noise \(e_n(f_H)\) with the ratio. When \(1\,\mathrm{kHz}\) and \(10\,\mathrm{kHz}\) are used, report those values explicitly; do not present them as universal detector standards.

Bottom line: a two-frequency ratio is a fast, repeatable heuristic for identifying photoconductors whose low-frequency excess noise reaches farther into the normal test band than it does in comparable devices.

Sources

References and further reading

  1. C. T. Lin, Y. K. Su, S. J. Chang, H. T. Huang, S. M. Chang, and T. P. Sun, “Effects of passivation and extraction surface trap density on the 1/f noise of HgCdTe photoconductive detector,” IEEE Photonics Technology Letters, vol. 9, no. 2, pp. 232–234, 1997. doi:10.1109/68.553102.
  2. National Institute of Standards and Technology, “Flicker Noise,” Time and Frequency from A to Z. NIST definition and terminology.
  3. Zurich Instruments, “Lock-in Tab,” UHF User Manual. The manual distinguishes noise-equivalent power bandwidth from the \(3\,\mathrm{dB}\) bandwidth and documents filter settings relevant to noise normalization. Instrument documentation.

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